that the Air Force is acknowledging that they didn't file the paperwork correctly and is trying to find out why to determine if it is a systemic issue or simply an example of human error.

I suspect that it is a manual thing rather than some sort of automatic process. I suspect that some soldier/sailor/airman/marine/coastie has to manually input the outcome of the court martial into some file to submit to NICS. I doubt that it is as automated as we see in many Hollywood police dramas.

And while I'm certainly no expert, it is my recollection that it isn't an absolute, so MOST,(but not all) dishonorable discharges would render a person ineligible to purchase a firearm. But since it isn't ALL, they may not be able to create a system that does it automatically.